Worksheet: Transformations of Quadratic Functions
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1 Worksheet: Transformations of Quadratic Functions Multiple Choice Identif the choice that best completes the statement or answers the question.. Which correctl identifies the values of the parameters a, h, and k for the function. What is the equation of this graph? x Which function includes a translation of units to the left?. Which equation shows a translation of left and vertical compression b a factor of to the graph of?. Joanne hit a ball straight up into the air. The height of the ball in metres, is given b the function t seconds after the ball is hit. In how man seconds will the ball hit the ground? a. c. 9 b. 6 d. 6. Kevin threw a ball straight up with an initial speed of 0 metres per second. The function describes the ball s height, in metres, t seconds after Kevin threw it. What are the coordinates of the vertex? (0, ) 7. Which equation describes a parabola that opens downward, is congruent to, and has its vertex at (0, )?
2 8. List the sequence of steps required to graph the function a. horizontal translation units to the right, vertical compression b a factor of, vertical translation 6 units down b. horizontal translation units to the right, reflection in x-axis, vertical translation 6 units down c. horizontal translation units to the left, vertical translation 6 units up, reflection in x-axis d. horizontal translation units to the left, reflection in x-axis, vertical translation 6 units down 9. Which function matches the graph? x 0. Consider a parabola P that is congruent to, opens upward, and has vertex. Now find the equation of a new parabola that results if P is reflected in the x-axis and translated units down.. The graphs of and another parabola are shown below. What is a possible equation for the second parabola?
3 =x =? x Short Answer. The graph of f(x) is shown below. Graph the transformed functions in the same set of axes. x. Name a function to describe each graph. GRAPH A
4 f(x) =? f(x)=x^ x GRAPH B f(x)=x^ g(x)=? x. How does the shape of the graph of compare with the graph of? Explain.. The net annual income of an engineer in Barr s compan can be modelled b, where x is the age of the engineer and. What is the axis of smmetr? 6. Sketch the final graph of the function, Problem 7. A parabola that opens downward has its vertex at (, 0) and a -intercept at (0, 9) The parabola is congruent to the parabola described b the function a) What is the equation of the function? b) Draw a graph of the function using ke points. c) What is the axis of smmetr?
5 d) What are the values of the parameters a, h, and k? Worksheet: Transformations of Quadratic Functions Answer Section MULTIPLE CHOICE. ANS: C PTS: REF: Knowledge and Understanding OBJ:. - Graphing Quadratic Functions b Using Transformations. ANS: D PTS: REF: Knowledge and Understanding OBJ:. - Graphing Quadratic Functions b Using Transformations. ANS: A PTS: REF: Knowledge and Understanding OBJ:. - Graphing Quadratic Functions b Using Transformations. ANS: D PTS: REF: Knowledge and Understanding OBJ:. - Graphing Quadratic Functions b Using Transformations. ANS: B PTS: REF: Application OBJ:. - Graphing Quadratic Functions b Using Transformations 6. ANS: B PTS: REF: Application OBJ:. - Graphing Quadratic Functions b Using Transformations 7. ANS: B PTS: REF: Knowledge and Understanding OBJ:. - Graphing Quadratic Functions b Using Transformations 8. ANS: D PTS: REF: Communication OBJ:.6 - Using Multiple Transformations to Graph Quadratic Functions 9. ANS: B PTS: REF: Knowledge and Understanding OBJ:.6 - Using Multiple Transformations to Graph Quadratic Functions 0. ANS: C PTS: REF: Knowledge and Understanding OBJ:.6 - Using Multiple Transformations to Graph Quadratic Functions. ANS: A PTS: REF: Application OBJ:.6 - Using Multiple Transformations to Graph Quadratic Functions SHORT ANSWER. ANS: x PTS: REF: Knowledge and Understanding
6 OBJ:. - Graphing Quadratic Functions b Using Transformations. ANS: Answers ma var. For example: Graph A: Graph B: PTS: REF: Thinking OBJ:. - Graphing Quadratic Functions b Using Transformations. ANS: compressed verticall b a factor of and reflec- The shape of the graph is the same as the graph of ted verticall. PTS: REF: Communication OBJ:. - Graphing Quadratic Functions b Using Transformations. ANS: PTS: REF: Application OBJ:. - Graphing Quadratic Functions b Using Transformations 6. ANS: x PTS: REF: Knowledge and Understanding OBJ:.6 - Using Multiple Transformations to Graph Quadratic Functions PROBLEM 7. ANS: a)
7 6 7 x 6 7 b) c) d) 8 PTS: REF: Communication OBJ:. - Graphing Quadratic Functions b Using Transformations
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